A272758 Perfect powers whose binary reversal is also a perfect power.

1, 4, 8, 9, 16, 27, 32, 36, 64, 128, 144, 216, 256, 512, 576, 1024, 1728, 2048, 2304, 4096, 8192, 9216, 13824, 16384, 32768, 36864, 65536, 110592, 131072, 147456, 262144, 524288, 589824, 884736, 1048576, 2097152, 2359296, 4194304, 7077888, 8388608, 9437184, 16777216

Offset

1,2

Comments

All powers of 2 (A000079) are terms. - Michel Marcus, May 06 2016

Links

Amiram Eldar, Table of n, a(n) for n = 1..140

Example

The binary expansion of 16=2^4 is 10000, its reversal is 1, a square, so 16 is a term.

Mathematica

fQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[Select[Range[2^20], fQ], fQ@ FromDigits[Reverse@ IntegerDigits[#, 2], 2] &] (* Michael De Vlieger, May 05 2016, after Ant King and Robert G. Wilson v at A001597 *)

Prog

(PARI) isp(n) = (n==1) || ispower(n);
isok(n) = isp(n) && isp(subst(Polrev(binary(n)), x, 2)); \\ Michel Marcus, May 06 2016

Crossrefs

Cf. A000079, A001597, A030101, A118895 (base-10 analog).

Sequence in context: A348995 A324723 A355580 * A227645 A285438 A089042

Adjacent sequences: A272755 A272756 A272757 * A272759 A272760 A272761

Keyword

nonn,base

Author

Benjamin Przybocki, May 05 2016

Status

approved